Question: Solve for $x$ and $y$ using elimination. ${x-4y = -25}$ ${-x-3y = -31}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $-7y = -56$ $\dfrac{-7y}{{-7}} = \dfrac{-56}{{-7}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {x-4y = -25}\thinspace$ to find $x$ ${x - 4}{(8)}{= -25}$ $x-32 = -25$ $x-32{+32} = -25{+32}$ ${x = 7}$ You can also plug ${y = 8}$ into $\thinspace {-x-3y = -31}\thinspace$ and get the same answer for $x$ : ${-x - 3}{(8)}{= -31}$ ${x = 7}$